We propose two novel axioms for qualitative probability spaces (Bernstein, 1917; de Finetti, 1937; Koopman, 1940; Savage, 1954): (i) unlikely atoms, which requires that there is an event containing no atoms that is at least as likely as its complement; and (ii) third-order atom-swarming, which requires that...

We investigate menu mechanisms: dynamic mechanisms where at each history, an agent selects from a menu of his possible assignments. We consider both ex-post implementation and full implementation, for both subgame perfection and a strengthening of dominance that covers off-path histories, and...